The Norwegian Academy of Science and Letters named John Milnor the 2011 recipient of the Abel Prize "for his pioneering discoveries in topology, geometry and algebra."

John Milnor has received many awards and honours. He received the Fields Medal in 1962 for his work in differential topology when he was only 31. He was awarded the 2011 Leroy P. Steele Prize for Lifetime Achievement by the American Mathematical Society. Milnor has previously won two other Steele Prizes from the AMS: for Mathematical Exposition (2004) and for Seminal Contribution to Research (1982). In 1989 Milnor received the Wolf Prize in Mathematics. John Milnor received the US National Medal of Science in 1967. He was elected as a member of the National Academy of Sciences in 1963. Since 1994, he has been a foreign member of the Russian Academy of Sciences, and in 2004 he became a member of the European Academy of Sciences, Arts and Letters.